Latitude and Longitude General Information CALCULATORS and CONVERTERS | Back Latitude and Longitude General Information The earth is effectively a sphere, so how do we describe where a point is on its surface? The most common way to locate points on the surface of the Earth is by standard, geographic coordinates called latitude and longitude. These coordinates values are measured in degrees (of arc, not temperature), and represent angular distances calculated from the center of the Earth. However, there are several CORRECT ways to designate them and to use the different values. What is latitude? We can imagine the Earth as a sphere, with an axis around which it spins. The ends of the axis are the North and South Poles. The Equator is a line around the earth, an equal distance from both poles. The Equator is also the latitude line given the value of zero degrees. This means it is the starting point for measuring latitude, up and down, or North and South properly indicated. Latitude values indicate the angular distance between the Equator and points North or South of it on the surface of the Earth. A line connecting all the points with the same latitude value is called a line of latitude. This term is usually used to refer to the lines that represent values in whole degrees.

All lines of latitude are parallel to the Equator (and to each other), and they are sometimes also referred to as parallels. Parallels are equally spaced but they do NOT have the same distance around them! There are 90 degrees of latitude going North from the Equator, and the North Pole is at 90 degrees N. There are 90 degrees to the South of the Equator, and the South Pole is at 90 degrees S. Both are obviously the most distant points from any point on the Equator. When the directional designators (N, S, E or W) are omitted, northern latitudes are given positive values and southern latitudes are given negative values. The Prime Meridian is the alpha and omega of the lines of longitude, called meridians. They run perpendicular to lines of latitude, and all pass through both poles. Each longitude line is part of a great circle. There is no obvious zero degree point for longitude, as there is for latitude. Throughout history many different starting points have been used to measure longitude. By international agreement, the meridian line through Greenwich, England, is currently given the value of zero degrees of longitude; this meridian is referred to as the Prime Meridian.

Longitude values are indicate the angular distance between the Prime Meridian and points east or west of it on the surface of the Earth. The Earth is divided equally into 360 degrees of longitude. There are 180 degrees of longitude to the east of the Prime Meridian; when the directional designator is omitted these longitudes are given positive values. There are also 180 degrees of longitude to the west of the Prime Meridian; when the directional designator is omitted these longitudes are given negative values. The 180 degree longitude line is opposite the Prime Meridian on the globe, and is the same going either east or west. How precise can we be with latitude and longitude? Degrees of latitude and longitude can be further subdivided into minutes and seconds (units of arc, not time): There are 60 minutes (') per degree, and 60 seconds (") per minute. For example, a coordinate might be written 65° 32' 15".

Degrees can also be expressed as decimals: 65.5375, degrees and decimal minutes: 65° 32.25', or even degrees, minutes, and decimal seconds: 65° 32' 15.275". All these notations allow us to locate places on the Earth quite precisely – to within inches, depending on the accuracy of the equipment doing the measurement. A degree of latitude is approximately 69 miles, and a minute of latitude is approximately 1.15 miles. A second of latitude is approximately 0.02 miles, or just over 100 feet. A degree of longitude varies in size. At the equator, it is approximately 69 miles, the same size as a degree of latitude. The size gradually decreases to zero as the meridians converge at the poles. At a latitude of 45 degrees, a degree of longitude is approximately 49 miles. Because a degree of longitude varies in size, minutes and seconds of longitude also vary, decreasing in size towards the poles. We suggest that you take a look at our various GPS and longitude and latitude calculators.

With the maturity of GPS, the importance and availability of latitude and longitude information is within the reach and grasp of most of us. All of our tools do things that are different from each other, or have a different methodology, if similar. Our Geography Calculators and Converters start page is an ideal place to begin. Also Look at our Aviation Calculators and Converters , Marine Calculators and Converters , Weather Calculators and Converters and Automotive Calculators and Converters . Our Special Latitude and Longitude information calculator and converter will give you much of the knowledge to work with all of our other converters and calculators on the site. Leave us a question or comment on Facebook Search or Browse Our Site 02 - Portraying the Earth - The geographic grid is used to accurately measure 02 - Portraying the Earth 02 - Portraying the Earth - The geographic grid is used to... SCHOOL View Full Document This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The geographic grid is used to accurately measure location on Earths surface Grid of intersecting lines used to fix specific location on a sphere (360) Note: Every square meter on Earths surface has it own address relative to the geographic grid Latitude angular distance (degrees) north or south of the equator Parallel line connecting all points along the same latitude Longitude is the angular distance (degrees) east or west of a prime meridian Meridian line connecting all points along the same longitude Example: Callcott Building Located exactly at 33 59 46 N, 81 1 34 W Reads as: 33 degrees 59 minutes 4 seconds north of the Equator, 81 degrees 1 minute 3 seconds west of the Prime Meridian Prime Meridian &amp; Standard Time Earth revolves 360 eastward every 24 hours or 15 per hour 1 hour time zones that span 7.5 on both sides of a central meridian Maps are generalized views of an area Useful for analyzing spatial relationships Cartography mapmaking...

Energy Transfer Factors Affecting Insolation Atmospheric Warming/The Greenhouse Ef 05 - Energy Transfer Earth Coordinate System Great Circles: The shortest path between two points on a plane is a straight line. On the surface of a sphere, however, there are no straight lines. The shortest path between two points on the surface of a sphere is given by the arc of the great circle passing through the two points. A great circle is defined to be the intersection with a sphere of a plane containing the center of the sphere. Two great circles If the plane does not contain the center of the sphere, its intersection with the sphere is known as a small circle. In more everyday language, if we take an apple, assume it is a sphere, and cut it in half, we slice through a great circle. If we make a mistake, miss the center and hence cut the apple into two unequal parts, we will have sliced through a small circle. Two small circles Spherical Triangles: If we wish to connect three points on a plane using the shortest possible route, we would draw straight lines and hence create a triangle. For a sphere, the shortest distance between two points is a great circle.

By analogy, if we wish to connect three points on the surface of a sphere using the shortest possible route, we would draw arcs of great circles and hence create a spherical triangle. To avoid ambiguities, a triangle drawn on the surface of a sphere is only a spherical triangle if it has all of the following properties: The three sides are all arcs of great circles. Any two sides are together greater than the third side. The sum of the three angles is greater than 180°. Each spherical angle is less than 180°. Hence, in figure below, triangle PAB is not a spherical triangle (as the side AB is an arc of a small circle), but triangle PCD is a spherical triangle (as the side CD is an arc of a great circle). You can see that the above definition of a spherical triangle also rules out the "triangle" PCED as a spherical triangle, as the vertex angle P is greater than 180° and the sum of the sides PC and PD is less than CED. The figure below shows a spherical triangle, formed by three intersecting great circles, with arcs of length (a,b,c) and vertex angles of (A,B,C).

Note that the angle between two sides of a spherical triangle is defined as the angle between the tangents to the two great circle arcs, as shown in the figure below for vertex angle B. Earth's Surface: The rotation of the Earth on its axis presents us with an obvious means of defining a coordinate system for the surface of the Earth. The two points where the rotation axis meets the surface of the Earth are known as the north pole and the south pole and the great circle perpendicular to the rotation axis and lying half-way between the poles is known as the equator. Great circles which pass through the two poles are known as meridians and small circles which lie parallel to the equator are known as parallels or latitude lines. The latitude of a point is the angular distance north or south of the equator, measured along the meridian passing through the point. A related term is the co-latitude, which is defined as the angular distance between a point and the closest pole as measured along the meridian passing through the point. In other words, co-latitude = 90° - latitude.

Distance on the Earth's surface is usually measured in nautical miles, where one nautical mile is defined as the distance subtending an angle of one minute of arc at the Earth's center. A speed of one nautical mile per hour is known as one knot and is the unit in which the speed of a boat or an aircraft is usually measured. Horizon System: Humans perceive in Euclidean space -> straight lines and planes. But, when distances are not visible (i.e. very large) than the apparent shape that the mind draws is a sphere -> thus, we use a spherical coordinate system for mapping the sky with the additional advantage that we can project Earth reference points (i.e. North Pole, South Pole, equator) onto the sky. Note: the sky is not really a sphere! From the Earth's surface we envision a hemisphere and mark the compass points on the horizon. The circle that passes through the south point, north point and the point directly over head (zenith) is called the meridian. This system allows one to indicate any position in the sky by two reference points, the time from the meridian and the angle from the horizon. Of course, since the Earth rotates, your coordinates will change after a few minutes.

The horizontal coordinate system (commonly referred to as the alt-az system) is the simplest coordinate system as it is based on the observer's horizon. The celestial hemisphere viewed by an observer on the Earth is shown in the figure below. The great circle through the zenith Z and the north celestial pole P cuts the horizon NESYW at the north point (N) and the south point (S). The great circle WZE at right angles to the great circle NPZS cuts the horizon at the west point (W) and the east point (E). The arcs ZN, ZW, ZY, etc, are known as verticals. The two numbers which specify the position of a star, X, in this system are the azimuth, A, and the altitude, a. The altitude of X is the angle measured along the vertical circle through X from the horizon at Y to X. It is measured in degrees. An often-used alternative to altitude is the zenith distance, z, of X, indicated by ZX. Clearly, z = 90 - a. Azimuth may be defined in a number of ways.

For the purposes of this course, azimuth will be defined as the angle between the vertical through the north point and the vertical through the star at X, measured eastwards from the north point along the horizon from 0 to 360°. This definition applies to observers in both the northern and the southern hemispheres. It is often useful to know how high a star is above the horizon and in what direction it can be found - this is the main advantage of the alt-az system. The main disadvantage of the alt-az system is that it is a local coordinate system - i.e. two observers at different points on the Earth's surface will measure different altitudes and azimuths for the same star at the same time. In addition, an observer will find that the star's alt-az coordinates changes with time as the celestial sphere appears to rotate. Despite these problems, most modern research telescopes use alt-az mounts, as shown in the figure above, owing to their lower cost and greater stability. This means that computer control systems which can transform alt-az coordinates to equatorial coordinates are required.

Celestial Sphere: The celestial sphere has a north and south celestial pole as well as a celestial equator which are projected reference points to the same positions on the Earth surface. Right Ascension and Declination serve as an absolute coordinate system fixed on the sky, rather than a relative system like the zenith/horizon system. Right Ascension is the equivalent of longitude, only measured in hours, minutes and seconds (since the Earth rotates in the same units). Declination is the equivalent of latitude measured in degrees from the celestial equator (0 to 90). Any point of the celestial (i.e. the position of a star or planet) can be referenced with a unique Right Ascension and Declination. The celestial sphere has a north and south celestial pole as well as a celestial equator which are projected from reference points from the Earth surface. Since the Earth turns on its axis once every 24 hours, the stars trace arcs through the sky parallel to the celestial equator. The appearance of this motion will vary depending on where you are located on the Earth's surface. Note that the daily rotation of the Earth causes each star and planet to make a daily circular path around the north celestial pole referred to as the diurnal motion.

Equatorial Coordinate System : Because the altitude and azimuth of a star are constantly changing, it is not possible to use the horizontal coordinate system in a catalog of positions. A more convenient coordinate system for cataloging purposes is one based on the celestial equator and the celestial poles and defined in a similar manner to latitude and longitude on the surface of the Earth. In this system, known as the equatorial coordinate system, the analog of latitude is the declination, δ. The declination of a star is its angular distance in degrees measured from the celestial equator along the meridian through the star. It is measured north and south of the celestial equator and ranges from 0° at the celestial equator to 90° at the celestial poles, being taken to be positive when north of the celestial equator and negative when south. In the figure below, the declination of the star X is given by the angle between Y and X. The analog of longitude in the equatorial system is the hour angle, H (you may also see the symbol HA used).

Defining the observer's meridian as the arc of the great circle which passes from the north celestial pole through the zenith to the south celestial pole, the hour angle of a star is measured from the observer's meridian westwards (for both northern and southern hemisphere observers) to the meridian through the star (from 0° to 360°). Because of the rotation of the Earth, hour angle increases uniformly with time, going from 0° to 360° in 24 hours. The hour angle of a particular object is therefore a measure of the time since it crossed the observer's meridian - hence the name. For this reason it is often measured in hours, minutes and seconds of time rather than in angular measure (just like longitude). In figure above, the hour angle of the star X is given by the angle Z-NCP-X. Note that all stars attain their maximum altitude above the horizon when they transit (or attain upper culmination on, in the case of circumpolar stars) the observers meridian. The declination of a star does not change with time. The hour angle does, and hence it is not a suitable coordinate for a catalogue.

This problem is overcome in a manner analogous to the way in which the Greenwich meridian has been (arbitrarily) selected as the zero point for the measurement of longitude. The zero point chosen on the celestial sphere is the first point of Aries, γ, and the angle between it and the intersection of the meridian through a celestial object and the celestial equator is called the right ascension (RA) of the object. Right ascension is sometimes denoted by the Greek letter α and is measured from 0h to 24h along the celestial equator eastwards (in the direction of a right-handed screw motion about the direction to the north celestial pole) from the first point of Aries, that is, in the opposite direction to that in which hour angle is measured. Like the definition of hour angle, this convention holds for observers in both northern and southern hemispheres. In above figure, the right ascension of the star X is given by the angle -NCP-Y. Most modern research telescopes do not use equatorial mounts due to their higher cost and lower stability.

This is at the expense of the simplicity of telescope tracking - an equatorially-mounted telescope need only move its right ascension axis in order to track the motion of the celestial sphere. The figure above shows an example of an equatorially-mounted telescope. The above diagram displays the typical motion of a star or planet in the sky, with the relevant angles marked. The star, X, crosses the horizon at L and V, traveling from L through U on the meridian, down to V. H is the hour angle of the star, which will equal the arc BT, but not the arc XU. Constellations: Drawn onto the celestial sphere are imaginary shapes called constellations, Latin for `group of stars'. Due to the nature of the Earth's surface, the sky is divided into the northern and southern sky as seen from each hemisphere. Northern Sky Southern Sky Constellations are often drawn in the shapes of mythical heros and creatures tracing a pattern of stars on the celestial sphere, recorded on a star map . The origin of the names of particular constellations is lost with time, dating back before written records. The ancient Greeks were the first to record the oral legends.

But the boundaries of the constellations were fixed by the International Astronomical Union in 1928. For many of the constellations it is easy to see where they got their names. For example, Aquila, the Eagle Hercules, the Warrior Scorpius, the Scorpion In all, there are 88 constellation names cataloged by Hipparchus in 100 B.C. To find out more about your favorite constellation, goto Constellation of the Month . Since the boundaries are fixed, a star will always remain in a constellation unless its proper motion moves it into another. Star Names: Hipparchus also developed a simply method of identifying the stars in the sky by using a letter from the Greek alphabet combined with the constellation name. So, for example, the brightest star in the constellation Orion is Alpha Orion, the second brightest star is Beta Orion, and so on. When the letters run out, we use a number 33 Orion, 101 Orion, etc. Some of the very brightest stars have their own names due to their importance to early navigators. For example, Alpha Canis Major is Sirius, the Dog Star.

About 6000 stars are visible with the naked eye on a dark, moonless night. However, there are over 1013 stars in the whole Milky Way galaxy were the solar system resides. Thus, we only see a very small fraction of the closest and brightest stars with our eyes. The first star catalog was published by Ptolemy in the 2nd century. It contained the positions of 1025 of the brightest stars in the sky. The first modern star catalog was the Bonner Durchmusterung by Argelander in 1860, containing 320,000 stars. Since the Earth's axis is tilted 23 1/2 degrees from the plane of our orbit around the Sun, The apparent motion of the Sun through the sky during the year is a circle that is inclined 23 1/2 degrees from the celestial equator. This circle is called the ecliptic and passes through 12 of the 88 constellations that we call the zodiac . Equinox and Solstice: The projection of the Sun's path across the sky during the year is called the ecliptic.

The points where the ecliptic crosses the celestial equator are the vernal and autumnal equinox's. The point were the Sun is highest in the northern hemisphere is called the summer solstice. The lowest point is the winter solstice. Days are longest in the summer for the northern hemisphere due to tilt of the Earth's axis allowing for more sunlight to be projected onto surface. Note also the reason for the "midnight" sun at the North Pole in summer. Longest day of the year is at the summer solstice For opposite reasons, days are short and nights long in the winter. Seasons: The seasons are caused by the angle the sun's rays make with the ground. Higher Sun angle means more luminosity per square meter. Low Sun angle produces fewer rays per square meter. More intensity means more heat and, therefore, higher temperatures. Note that, due to the fact that our oceans store heat, the actual changes in mean Earth temperature are delayed by several weeks, i.e. the hottest days of summer are usually in late July, over a month from the summer solstice. Sidereal and Synodic time: A `day' is defined by the rotation of object in question.

For example, the Moon's `day' is 27 Earth days. A `year' is defined by the revolution of object in question. For example, the Earth's year is 365 days divided into months ; whereas, Pluto's `year' is 248.6 Earth years. Typical we use synodic time, which means with respect to the Sun, in our everyday life. For example, noon, midnight, twilight are all examples of synodic time based on where the Sun is in the sky (e.g. directly overhead on the equator for noon). Astronomers often use sidereal time, which means time with respect to the stars, for their measurements. Since the Earth moves around the Sun once every 365 days, the Sun's apparent position in the sky changes from day to day. Note, in the above diagram, we see that the Earth's synodic day is 4 mins longer than its sidereal day. Phases of the Moon: The Moon is tidally locked to the Earth, meaning that one side always faces us (the nearside), whereas the farside is forever hidden from us.

In addition, the Moon is illuminated on one side by the Sun, the other side is dark (night). Which parts are illuminated (daytime) and which parts we see from the Earth are determined by the Moon's orbit around the Earth, what is called the phase of the Moon (click here for the current phase of the Moon). As the Moon moves counterclockwise around the Earth, the daylight side becomes more and more visible (i.e. we say the Moon is ` waxing '). After full Moon is reached we begin to see more and more of the nighttime side (i.e. we say the Moon is `waning'). This whole monthly sequence is called the phases of the Moon . Eclipses: On rare occasions the Moon comes between the Earth and the Sun (a solar eclipse ) or the Moon enters the Earth's shadow (a lunar eclipse ). Eclipses only occur when the line of nodes is aligned with the Sun (2 to 5 times a year). All solar eclipses occur at new moon with a duration of only 4 to 7 mins. The path of shadow across surface of the Earth determines who gets to see it.

All lunar eclipses occur at full moon and everyone on nightside of Earth is able to observe lunar eclipses. The deep red color during the eclipse comes from light refracted through Earth's atmosphere (i.e. red sunset's) How to Calculate the Velocity of the Earth's Rotation | eHow How to Calculate the Velocity of the Earth's Rotation Ryan McVay/Stockbyte/Getty Images Physicists calculate the velocity of an object as its change in position divided by the time elapsed during that change. In the case of the Earth (a sphere spinning on an axis), the distance traveled in one day represents the circumference of the earth and the elapsed time is about 24 hours. However, the circumference changes depending on the point on the earth’s surface used as a reference. For example, a point on the Earth’s equator travels much faster than a point near one of the poles. Things You'll Need Calculator Calculate the velocity of the earth’s rotation at its equator by dividing the circumference at the equator (24,902 miles) by the time required for the earth to make one full rotation (23 hours and 56 minutes, or 23.93 hours).

The velocity is therefore 24,902 / 23.93 = 1041 (rounded) miles per hour. Find the latitude of any location on the earth’s surface other than the equator by referring to a map or an online database, such as that provided in the Resources. For example, Phoenix, Arizona sits at 33 degrees, 26 minutes north latitude. Convert this value to decimal form by dividing the minutes by 60 and adding this value to the degrees. In this case, 26 / 60 = 0.43. The latitude of Phoenix is therefore 33.43 degrees. Calculate the rotational velocity of the earth at the location of your choice by first taking the cosine of the location’s latitude in degrees and then multiplying this value by the earth’s rotational velocity at the equator. Use the cosine button on a scientific calculator to find the cosine from the degrees. In the case of Phoenix, cos(33.43) = 0.8346 (rounded). The rotational velocity is therefore 0.8346 * 1041 = 869 (rounded) miles per hour.

Celestial Sphere THE CELESTIAL SPHERE We observe the sky as it looks, not as it is. You feel like you are on top of the Earth (the result of gravity drawing you toward the Earth's center). In the example, you are at a latitude (your location along an arc from the Earth's equator to the rotation pole, given by lower case Greek letter Phi) of 45°, halfway between the Earth's equator and the north pole. The latitude of the north pole is 90°, that of the equator 0°. The Earth appears to lie at the center of a fictional celestial sphere. You pretend that you are inside the sphere at the center looking out around you. Above your head is your zenith, while directly below you is your nadir (both of which are points on the celestial sphere). In between is the great circle of the horizon, which is the circle on the celestial sphere cut by a plane tangent to the Earth at your feet. Everything in the sky above the horizon is visible, while everything below it is not. The celestial sphere is tipped relative to the observer in the same way as is the Earth.

The extension of the Earth's rotation axis to the sky defines the North and South Celestial Poles (the NCP and SCP), while the extension of the Earth's equatorial plane defines the celestial equator. The NCP is in the constellation Ursa Minor (the Smaller Bear) close to the direction of the star Polaris , otherwise called the North Star. The SCP is in the modern constellation Octans , the Octant, in the general direction of the faint southern pole star Sigma Octantis (Polaris Australis). The circle that runs through the zenith, nadir, NCP, and SCP is the celestial meridian. The intersection of the celestial meridian and the horizon define north (N) and south (S), while that between the equator and the horizon define east (E) and west (W). The intersection of the celestial meridian and the celestial equator (upper case Greek letter Sigma) is down from the zenith by an angle equal to the latitude. The Earth rotates about its poles from west to east (counterclockwise as viewed from above the north pole), which makes the sky seem to rotate in the other direction about the north and south celestial poles parallel to the celestial equator.

The elevation above the horizon (the altitude) of the NCP always equals the observer's latitude. If you are in the southern hemisphere, the south celestial pole (the SCP) is above the horizon, the NCP below it. A star on the celestial sphere seems to go around the observer on a daily path (red circle). The perpendicular angle of a star north or south of the celestial equator is given by its declination, indicated by lower case Greek letter Delta. When the star drops below the horizon, it sets, while when it comes up above the horizon it rises. A star on the celestial equator rises exactly east, sets exactly west. The greater the declination, the farther north of west the star both sets and rises. If far enough north (declination 90° - latitude), the star misses the horizon and is circumpolar, that is, always visible. If the declination is far enough south, the star does not get above the horizon and is always invisible.

THE ECLIPTIC Though in truth the Earth orbits the Sun , we feel stationary, which makes the Sun appear to go around the Earth once a year in the counterclockwise direction (from west to east, counter to its daily motion across the sky) along a steady path called the ecliptic. Since there are 365 (actually 365.2422...) days in the year, and 360° in the circle, the Sun moves to the east at the slow pace of only a bit under a degree per day. At the same time it is constantly moving (rather, appearing to move) from east to west as a result of the Earth's rotation, just at a pace slightly slower than the stars because of its simultaneous easterly drift. The perpendiculars to the ecliptic plane define the ecliptic poles. The North Ecliptic Pole (NEP) is in Draco , the South Ecliptic Pole (SEP) in Dorado . The Earth's axis is tilted relative to the perpendiculars to the ecliptic plane by an angle of 23.5° (actually closer to 23.4°).

The tilt separates the celestial and ecliptic poles by the same angle, which causes the circle of the ecliptic to be tilted relative to the celestial equator again by the same angle, which as a result is called the obliquity of the ecliptic. As it moves along the ecliptic against the background stars, which are there even if you cannot see them against the blue sky , the Sun therefore appears also to move north and south of the celestial equator. As the Sun traverses the ecliptic path, it appears to move against a band of 12 ancient constellations called the Zodiac, which are given in traditional order are shown below. The second line for each entry gives the average date on which the Sun enters the constellation according to the official boundaries established in 1930 by the International Astronomical Union. They depend somewhat on the proximity of a leap year. The modern boundary of Ophiuchus (the Serpent Bearer) is crossed by the ecliptic between Scorpius and Sagittarius, making it an unofficial thirteenth constellation of the Zodiac. It has no standing as part of the classical, traditional Zodiac, however. The Sun enters it November 30.

SUN AND SEASONS Twice a year, the Sun crosses the equator, on or about March 20 at a point called the Vernal Equinox, and on September 23 at the Autumnal Equinox (the terms derived from a northern hemisphere perspective). On these dates, the Sun has a declination of 0°, rises exactly east, sets exactly west, is up for 12 hours and down for 12 hours, hence the term equinox. The equinox passages respectively announce the beginning of northern- hemisphere spring and autumn (and southern hemisphere autumn and spring). (In actual fact, the risings, settings, and 12-hour durations cannot be exact, since the Sun is continuously moving along the ecliptic and is on the equinoxes but for the moment. In addition, upward refraction by the Earth's atmosphere and the finite angular diameter of the Sun renders the equinox day a bit longer than 12 hours, night a bit shorter, all the while ignoring twilight.) As the Sun moves north of the equator from the Vernal Equinox, it rises and sets progressively more to the north of east and west. Days gradually become longer than 12 hours, nights shorter.

On June 21, the Sun reaches its most northerly extent (as seen in the right-hand "Earth" in the illustration), at a declination of 23.5 degrees north at the Summer Solstice, to begin northern- hemisphere summer (southern hemisphere winter). It then rises as far north of east and sets as far north of west as possible. Northern hemisphere days are now the longest of the year, nights the shortest, the extent of the effect dependent on latitude. Conversely, following the autumnal equinox, as the Sun moves south, it rises and sets progressively farther south of east and west. Northern hemisphere days now get shorter (less than 12 hours), nights longer (greater than 12 hours). On December 22, the Sun reaches its most southerly extent (see the left-hand "Earth"), at a declination of 23.5 degrees south, at the Winter Solstice to begin northern-hemisphere winter (southern hemisphere summer). It then rises as far south of east and sets as far south of west as possible. Northern-hemisphere daytime is now minimized, nighttime maximized.

All the effects are reversed in the southern hemisphere, while at the Earth's equator, days and nights are always equal at 12 hours. When at the Summer Solstice, the northern-hemisphere Sun (north of the tropics) crosses the celestial meridian as high as possible, while at the Winter Solstice it crosses as far to south as possible. In the summer, sunlight spreads itself over a smaller area of ground than it does in winter, and thereby heats the ground more efficiently, yielding more heat, so it is hot in the summer, cold in the winter. This effect is the sole cause of the Seasons . (The effect of the variation in distance between the Earth and the Sun caused by the Earth's elliptical orbit is of little consequence because of the power of the oceans to store heat.) Above the Arctic Circle at latitude 66.6° north (and below the Antarctic Circle, latitude 66.6° south), the Sun can be circumpolar in the summer, yielding 24 hours of sunlight and a midnight Sun ). The farther north of the Arctic Circle (or the farther south of the Antarctic Circle), the more days of midnight Sun you will see.

In the tropics (between latitudes 23.5°N at the Tropic of Cancer and 23.5°S at the Tropic of Capricorn) the Sun can be overhead sometime during the year (on June 21 at the former, on December 22 at the latter). TIME AND COORDINATES Your location on Earth is expressed through your latitude (your north-south position; see above) and longitude, which gives your east-west position. Draw a circle called a meridian from the north pole through your location to the south pole, then do the same through Greenwich, England to define the prime meridian, and note where they cross the equator. Your longitude (given by lower case Greek letter lambda) is the angle between the two intersections (of the meridians and the equator). In the illustration, the latitude of Greenwich is 51° 29' North (the longitude is by definition zero); those of Buenos Aries are 34° 35' South, 58° 29' West. There are 60 minutes (') in a degree of angle, 60 seconds (") in a minute.

The angular displacement of a star to the west of the celestial meridian (as measured along the celestial equator, analogous to longitude) is called the hour angle, which is usually given in time units at a rate of 15° per hour. Apparent solar time is given by the hour angle of the Sun plus 12 hours (the 12 hours added so that the "day" starts at midnight). Because of the eccentricity of the Earth's orbit and the obliquity of the ecliptic, apparent solar time does not keep a constant pace. Corrections for their effects lead to constant mean solar time, which can differ from apparent solar time by up to 17 minutes. The hour angle of the Sun, and therefore the time of day, varies continuously with longitude, wherein longitude differences exactly equal time differences. Standard times are the mean solar times of the closest standard meridians, which are displaced in units if 15° from Greenwich. (Political boundaries cause variances.) Star time, properly called sidereal time, is the hour angle of the Vernal Equinox.

Because the Sun moves to the east along the ecliptic, the Sun takes longer to make a circuit of the sky on its daily path than does a star or the equinox, so the solar day is 4 minutes longer than the sidereal day. As a result, the sidereal clock gains 4 minutes (actually 3 minutes 56 seconds) per day over the solar clock, starting from the time of solar passage across the autumnal equinox on September 23, when the two are the same. The right ascension of a star or any other celestial body (given by the lower-case Greek letter alpha) is the angle the body makes with the vernal equinox as measured to the east, again along the celestial equator. It too is usually measured in time units. The right ascension and hour angle of a body always add to equal the sidereal time. Given the sidereal time and the right ascension of a body, you can compute its hour angle, which with the declination allows you to set a telescope and to find anything in the sky.

The equinoxes and solstices are set against the background of the ancient zodiacal constellations: EQUINOXES AND SOLSTICES Sagittarius *But see below. Because of rotation, the Earth bulges slightly at its equator (greatly exaggerated in the drawing to the left; the difference between the equatorial and polar diameters is only 40 kilometers). The gravity of the Moon and Sun acting on the bulge causes the Earth's rotation axis to wobble around the perpendicular to its orbit with a period of 26,000 years, the phenomenon called precession. Precession causes the celestial poles (the NCP and the SCP) to move in circles around the ecliptic poles (the NEP and SEP), which changes the pole stars. In ancient Egyptian times, for example, the North Celestial Pole (NCP) pointed close to Thuban in Draco (the Dragon). Precession also causes the plane of the Earth's equator to wobble, which changes the directions of the equinoxes and solstices against the background stars (continuously altering the right ascensions and declinations of stars, though in a precisely known way).

In ancient times, the Vernal Equinox was in Aries , which is why that constellation tops the classical list. In classical times the Summer and Winter Solstices were in Cancer and Capricornus , hence the names "Tropic of Cancer" and "Tropic of Capricorn." Our astronomical roots are deep indeed. As a result of precession, around 1990 the Summer Solstice crossed the modern boundary from Gemini to Taurus, which now technically holds the point. Because the Summer Solstice is closer to the classic figure of Gemini than it is to that of Taurus, and since Gemini (along with Pisces, Libra, and Sagittarius) quarters the ecliptic, Gemini is still traditionally taken as the Solstice's celestial home. Figures are from STARS , James B. Kaler, Scientific American Library, Freeman, NY, copyright © James B. Kaler. To learn more about this subject, see The Ever-Changing Sky , James B. Kaler, Cambridge University Press, 2002. Copyright © James B. Kaler. All rights reserved.

These contents are the property of the author and may not be reproduced in whole or in part without the author's express consent except in fair use for educational purposes. Thanks to reader number . 2(b). Location, Distance, and Direction on Maps (b). Location, Distance, and Direction on Maps Location on Maps Most maps allow us to specify the location of points on the Earth's surface using a coordinate system. For a two-dimensional map, this coordinate system can use simple geometric relationships between the perpendicular axes on a grid system to define spatial location. Figure 2b-1 illustrates how the location of a point can be defined on a coordinate system. Figure 2b-1: A grid coordinate system defines the location of points from the distance traveled along two perpendicular axes from some stated origin. In the example above, the two axes are labeled X and Y. The origin is located in the lower left hand corner. Unit distance traveled along each axis from the origin is shown. In this coordinate system, the value associated with the X-axis is given first, following by the value assigned from the Y-axis. The location represented by the star has the coordinates 7 (X-axis), 4 (Y-axis).

Two types of coordinate systems are currently in general use in geography: the geographical coordinate system and the rectangular (also called Cartesian) coordinate system . Geographical Coordinate System The geographical coordinate system measures location from only two values, despite the fact that the locations are described for a three-dimensional surface. The two values used to define location are both measured relative to the polar axis of the Earth. The two measures used in the geographic coordinate system are called latitude and longitude . Figure 2b-2: Lines of latitude or parallels are drawn parallel to the equator (shown in red) as circles that span the Earth's surface. These parallels are measure in degrees (°). There are 90 angular degrees of latitude from the equator to each of the poles. The equator has an assigned value of 0°. Measurements of latitude are also defined as being either north or south of equator to distinguish the hemisphere of their location. Lines of longitude or meridians are circular arcs that meet at the poles. There are 180° of longitude either side of a starting meridian which is known the Prime Meridian . The Prime Meridian has a designated value of 0°.

Measurements of longitude are also defined as being either west or east of the Prime Meridian. Latitude measures the north-south position of locations on the Earth's surface relative to a point found at the center of the Earth (Figure 2b-2). This central point is also located on the Earth's rotational or polar axis . The equator is the starting point for the measurement of latitude. The equator has a value of zero degrees. A line of latitude or parallel of 30° North has an angle that is 30° north of the plane represented by the equator (Figure 2b-3). The maximum value that latitude can attain is either 90° North or South. These lines of latitude run parallel to the rotational axis of the Earth. Figure 2b-3: Measurement of latitude and longitude relative to the equator and the Prime Meridian and the Earth's rotational or polar axis. Longitude measures the west-east position of locations on the Earth's surface relative to a circular arc called the Prime Meridian (Figure 2b-2). The position of the Prime Meridian was determined by international agreement to be in-line with the location of the former astronomical observatory at Greenwich, England.

Because the Earth's circumference is similar to circle, it was decided to measure longitude in degrees. The number of degrees found in a circle is 360. The Prime Meridian has a value of zero degrees. A line of longitude or meridian of 45° West has an angle that is 45° west of the plane represented by the Prime Meridian (Figure 2b-3). The maximum value that a meridian of longitude can have is 180° which is the distance halfway around a circle. This meridian is called the International Date Line . Designations of west and east are used to distinguish where a location is found relative to the Prime Meridian. For example, all of the locations in North America have a longitude that is designated west. Universal Transverse Mercator System (UTM) Another commonly used method to describe location on the Earth is the Universal Transverse Mercator (UTM) grid system . This rectangular coordinate system is metric, incorporating the meter as its basic unit of measurement. UTM also uses the Transverse Mercator projection system to model the Earth's spherical surface onto a two-dimensional plane.

The UTM system divides the world's surface into 60 - six degree longitude wide zones that run north-south (Figure 2b-5). These zones start at the International Date Line and are successively numbered in an eastward direction (Figure 2b-5). Each zone stretches from 84° North to 80° South (Figure 2b-4). In the center of each of these zones is a central meridian. Location is measured in these zones from a false origin which is determined relative to the intersection of the equator and the central meridian for each zone. For locations in the Northern Hemisphere, the false origin is 500,000 meters west of the central meridian on the equator. Coordinate measurements of location in the Northern Hemisphere using the UTM system are made relative to this point in meters in eastings (longitudinal distance) and northings (latitudinal distance).

The point defined by the intersection of 50° North and 9° West would have a UTM coordinate of Zone 29, 500000 meters east (E), 5538630 meters north (N) (see Figures 2b-4 and 2b-5). In the Southern Hemisphere, the origin is 10,000,000 meters south and 500,000 meters west of the equator and central meridian, respectively. The location found at 50° South and 9° West would have a UTM coordinate of Zone 29, 500000 meters E, 4461369 meters N (remember that northing in the Southern Hemisphere is measured from 10,000,000 meters south of the equator - see Figures 2b-4 and 2b-5). Figure 2b-4: The following illustration describes the characteristics of the UTM zone "29" found between 12 to 6° West longitude. Note that the zone has been split into two halves.

The half on the left represents the area found in the Northern Hemisphere. The Southern Hemisphere is located on the right. The blue line represents the central meridian for this zone. Locations measurements for this zone are calculated relative to a false origin. In the Northern Hemisphere, this origin is located 500,000 meters west of the equator. The Southern Hemisphere UTM measurements are determined relative to a origin located at 10,000,000 meters south and 500,000 meters west of the equator and central meridian, respectively. The UTM system has been modified to make measurements less confusing. In this modification, the six degree wide zones are divided into smaller pieces or quadrilaterals that are eight degrees of latitude tall. Each of these rows is labeled, starting at 80° South, with the letters C to X consecutively with I and O being omitted (Figure 2b-5). The last row X differs from the other rows and extends from 72 to 84° North latitude (twelve degrees tall). Each of the quadrilaterals or grid zones are identified by their number/letter designation.

In total, 1200 quadrilaterals are defined in the UTM system. The quadrilateral system allows us to further define location using the UTM system. For the location 50° North and 9° West, the UTM coordinate can now be expressed as Grid Zone 29U, 500000 meters E, 5538630 meters N. Figure 2b-5: The UTM system also uses a grid system to break the Earth up into 1200 quadrilaterals. To keep the illustration manageable, most of these zones have been excluded. Designation of each quadrilaterals is accomplished with a number-letter system. Along the horizontal bottom, the six degree longitude wide zones are numbered, starting at 180° West longitude, from 1 to 60. The twenty vertical rows are assigned letters C to X with I and O excluded. The letter, C, begins at 80° South latitude. Note that the rows are 8 degrees of latitude wide, except for the last row X which is 12 degrees wide.

According to the reference system, the bright green quadrilateral has the grid reference 29V (note that in this system west-east coordinate is given first, followed by the south-north coordinate). This grid zone is found between 56 and 64° North latitude and 6 and 12° West longitude. Each UTM quadrilateral is further subdivided into a number of 100,000 by 100,000 meter zones. These subdivisions are coded by a system of letter combinations where the same two-letter combination is not repeated within 18 degrees of latitude and longitude. Within each of the 100,000 meter squares one can specify location to one-meter accuracy using a 5 digit eastings and northings reference system. The UTM grid system is displayed on all United States Geological Survey (USGS) and National Topographic Series (NTS) of Canada maps.

On USGS 7.5-minute quadrangle maps (1:24,000 scale), 15-minute quadrangle maps (1:50,000, 1:62,500, and standard-edition 1:63,360 scales), and Canadian 1:50,000 maps the UTM grid lines are drawn at intervals of 1,000 meters, and are shown either with blue ticks at the edge of the map or by full blue grid lines. On USGS maps at 1:100,000 and 1:250,000 scale and Canadian 1:250,000 scale maps a full UTM grid is shown at intervals of 10,000 meters. Figure 2b-6 describes how the UTM grid system can be used to determine location on a 1:50,000 National Topographic Series of Canada map. Figure 2b-6: The top left hand corner the "Tofino" 1:50,000 National Topographic Series of Canada map is shown above.

The blue lines and associated numbers on the map margin are used to determine location by way of the UTM grid system. Abbreviated UTM 1,000-meter values or principle digits are shown by numbers on the map margin that vary from 0 to 100 (100 is actually given the value 00). In each of the corners of the map, two of the principle digits are expressed in their full UTM coordinate form. On the image we can see 283000 m E. and 5458000 m N. The red dot is found in the center of the grid defined by principle numbers 85 to 86 easting and 57 to 58 northing. A more complete UTM grid reference for this location would be 285500 m E. and 5457500 m N. Information found on the map margin also tells us (not shown) that the area displayed is in Grid Zone 10U and the 100,000 m squares BK and CK are located on this map.

Distance on Maps In section 2a , w e have learned that depicting the Earth's three-dimensional surface on a two-dimensional map creates a number of distortions that involve distance, area, and direction. It is possible to create maps that are somewhat equidistance. However, even these types of maps have some form of distance distortion. Equidistance maps can only control distortion along either lines of latitude or lines of longitude . Distance is often correct on equidistance maps only in the direction of latitude. On a map that has a large scale, 1:125,000 or larger, distance distortion is usually insignificant. An example of a large-scale map is a standard topographic map. On these maps measuring straight line distance is simple. Distance is first measured on the map using a ruler. This measurement is then converted into a real world distance using the map's scale. For example, if we measured a distance of 10 centimeters on a map that had a scale of 1:10,000, we would multiply 10 (distance) by 10,000 (scale). Thus, the actual distance in the real world would be 100,000 centimeters.

Measuring distance along map features that are not straight is a little more difficult. One technique that can be employed for this task is to use a number of straight-line segments. The accuracy of this method is dependent on the number of straight-line segments used (Figure 2b-7). Another method for measuring curvilinear map distances is to use a mechanical device called an opisometer . This device uses a small rotating wheel that records the distance traveled. The recorded distance is measured by this device either in centimeters or inches. Figure 2b-7: Measurement of distance on a map feature using straight-line segments. Direction on Maps Like distance, direction is difficult to measure on maps because of the distortion produced by projection systems. However, this distortion is quite small on maps with scales larger than 1:125,000. Direction is usually measured relative to the location of North or South Pole . Directions determined from these locations are said to be relative to True North or True South . The magnetic poles can also be used to measure direction. However, these points on the Earth are located in spatially different spots from the geographic North and South Pole.

The North Magnetic Pole is located at 78.3° North, 104.0° West near Ellef Ringnes Island, Canada. In the Southern Hemisphere, the South Magnetic Pole is located in Commonwealth Day, Antarctica and has a geographical location of 65° South, 139° East. The magnetic poles are also not fixed overtime and shift their spatial position overtime. Topographic maps normally have a declination diagram drawn on them (Figure 2b-8). On Northern Hemisphere maps, declination diagrams describe the angular difference between Magnetic North and True North. On the map, the angle of True North is parallel to the depicted lines of longitude. Declination diagrams also show the direction of Grid North . Grid North is an angle that is parallel to the easting lines found on the Universal Transverse Mercator (UTM) grid system (Figure 2b-8). Figure 2b-8: This declination diagram describes the angular difference between Grid, True, and Magnetic North. This illustration also shows how angles are measured relative grid, true, and magnetic azimuth. In the field, the direction of features is often determined by a magnetic compass which measures angles relative to Magnetic North.

Using the declination diagram found on a map, individuals can convert their field measures of magnetic direction into directions that are relative to either Grid or True North. Compass directions can be described by using either the azimuth system or the bearing system. The azimuth system calculates direction in degrees of a full circle. A full circle has 360 degrees (Figure 2b-9). In the azimuth system, north has a direction of either the 0 or 360°. East and west have an azimuth of 90° and 270°, respectively. Due south has an azimuth of 180°. Figure 2b-9: Azimuth system for measuring direction is based on the 360 degrees found in a full circle. The illustration shows the angles associated with the major cardinal points of the compass. Note that angles are determined clockwise from north. The bearing system divides direction into four quadrants of 90 degrees. In this system, north and south are the dominant directions. Measurements are determined in degrees from one of these directions. The measurement of two angles based on this system are described in Figure 2b-10.

Figure 2b-10: The bearing system uses four quadrants of 90 degrees to measure direction. The illustration shows two direction measurements. These measurements are made relative to either north or south. North and south are given the measurement 0 degrees. East and west have a value of 90 degrees. The first measurement (green) is found in the north - east quadrant. As a result, its measurement is north 75 degrees to the east or N75°E. The first measurement (orange) is found in the south - west quadrant. Its measurement is south 15 degrees to the west or S15°W. Global Positioning Systems Determination of location in field conditions was once a difficult task. In most cases, it required the use of a topographic map and landscape features to estimate location. However, technology has now made this task very simple. Global Positioning Systems (GPS) can calculate one's location to an accuracy of about 30-meters (Figure 2b-11). These systems consist of two parts: a GPS receiver and a network of many satellites. Radio transmissions from the satellites are broadcasted continually.

The GPS receiver picks up these broadcasts and through triangulation calculates the altitude and spatial position of the receiving unit. A minimum of three satellite is required for triangulation. Figure 2b-11: Handheld Global Positioning Systems (GPS). GPS receivers can determine latitude, longitude, and elevation anywhere on or above the Earth's surface from signals transmitted by a number of satellites. These units can also be used to determine direction, distance traveled, and determine routes of travel in field situations.

Question: What name is given to your angular distance on the Earth's surface relative to the equator?
Answer: Latitude